Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?
a-3) a² + ab +3²
a + b) a ² - ab +6²
o a+ba? +la+b+Dab? - 53
a-ba? +da+b+Dab? - b​

The sum between the functions:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

is (f + g)(x) = 3x² + 5x + 2

Here we have two functions which are:

f(x) = 3x² - 2x + 6

g(x) = 7x - 4

And we want to add these to get f + g,  so we only need to add the two functions, we will get:

f(x) + g(x) = (3x² - 2x + 6) + (7x - 4)

Grouping like terms we will get:

(3x² - 2x + 6) + (7x - 4) = (3x²) + (-2x + 7x) + (6 - 4)

And now we can simplify that to get:

(3x²) + (-2x + 7x) + (6 - 4) = 3x² + 5x + 2

The sum is:

(f + g)(x) = 3x² + 5x + 2

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Answer:

Multiply all of the terms of each polynomial and then combine like terms. Example: Multiply: ( 2 x 2 + x − 3 ) ( x 2 − 2 x + 5 ) . Solution: Multiply each term of the first trinomial by each term of the second trinomial and then combine like terms.

Number of boys in Mandy’s science class is 5.

Now, According to the question:

The ratio of boys to girls in Mandy’s mathematics class is 3 to 12.

This ratio is the same in Mandy’s science class,

There are 20 girls.

To find the how many boys are there in Mandy’s science class?

Based on the given condition:

Let the ratio be 3x and 12x

Now, According to the statement:

12x = 20

x = 20/12

x = 5/3

So, Number of boys = 3 × 5/3 = 5

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One of the most important things to do to protect endangered animals is to reduce the amount of habitat destruction caused by human activities.

This can be done by creating protected areas and limiting or banning activities like logging, mining, or development in sensitive areas. Additionally, it is important to reduce over-hunting and poaching of these animals. This can be accomplished by establishing quotas and strict regulations on allowable hunting and fishing, as well as increasing enforcement efforts to catch violators. It is also important to understand the life cycles and behaviors of the threatened species so that we can better protect them. This can be done through field research, monitoring, and analyzing population trends. Finally, it is important to develop conservation plans and strategies to protect the species. These could include habitat restoration, reintroduction programs, captive breeding, and other measures to ensure their survival.

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Answer:

4 or 3

Step-by-step explanation:

X³+12X=7X²

X³-7X²+12X=0

X(X²-7X+12)=0

SOLVING THE QUADRATIC EQUATION

you have X=3 or X=4

A linear equation - y = 5x -7 is a slant line with intercepts for linear equations. A vertical line is x = 2. A line that runs through the origin is y = 3/4x.

A slant line with intercepts is y = 1/2x + 3. A horizontal line is y = 9. The line x = -1 runs vertically.

A direct condition is one that has a level of 1 as its most extreme worth. As a result, there is no variable in a linear equation with an exponent greater than 1. The graph of a linear equation will always be straight.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. As a result, this equation has intercepts and slant lines.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line actually traverses the origin. As a result, the origin of this equation is traversed by slant lines.

This line is not horizontal or vertical when the equation is graphed; rather, it is slant.

Additionally, this line does not traverse the origin. This equation is therefore a slant line with intercepts.

Since there is no x-intercept in this equation, it will be a horizontal line that runs parallel to the x-axis.

Additionally, this line does not traverse the origin. As a result, there is a horizontal line in this equation.

Since there is no y-intercept in this equation, it will be a vertical line that runs parallel to the y-axis.

Additionally, this line does not traverse the origin. As a result, this equation has a line that runs vertically.

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8) The Length of major arc MQN is; ⁵/₄πr

Length of minor arc MPN is; ³/₄πr

9) Length of major arc HJK is; ¹³/₁₅πr

Length of minor arc MPN is; ⁴/₁₅πr

The formula that is used to find the length of an arc is;

L = (θ/360) * 2πr

where;

L is length of arc

θ is central angle

r is radius

8) We are not given the radius and as such;

Length of major arc MQN = (225/360) * 2πr

= ⁵/₄πr

Length of minor arc MPN = ((360 - 225)/360) * 2πr

= ³/₄πr

9) Length of major arc HJK = (312/360) * 2πr

= ¹³/₁₅πr

Length of minor arc MPN = ((360 - 312)/360) * 2πr

= ⁴/₁₅πr

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Answer:

yes

Step-by-step explanation:

when y equals 0, x equals 0 also

y = x will produce a straight line passing through the point of origin (0,0)

The best estimate for the probability of getting tails is given as follows:

C Sue's estimate is best because she throws it more times than Eric.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

For this problem we calculate an experimental probability, as the outcomes are obtained from the previous trials of Eric and Sue.

The higher the number of trials, the closer the experimental probability is to the theoretical probability, meaning that the correct option is given by option C.

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Step-by-step explanation:

this creates a right-angled triangle 2.5 ft above the ground.

the string is the Hypotenuse (the side opposite to the 90° angle). the air distance to the height of the kite is one leg, and the height of the kite minus the 2.5 ft is leg 2.

in the trigonometric triangle the up/down side is sine (multiplied by the Hypotenuse or radius of the circle) of the angle at the center of the circle. and the left/right side is cosine (again multiplied by the Hypotenuse or radius) of the angle.

so, the height of the kite above ground is

105×sin(28°) + 2.5 = 51.79451409... ≈ 51.79 ft.

Answer:

give me brainlist please

Step-by-step explanation:

We can use the formula for conditional probability and the formula for the probability of the union of events to find P(C).

Using the formula for conditional probability, we can find P(A|B) = P(A n B) / P(B) = 0.05 / 0.26 = 0.192

Using the formula for conditional probability again, we can find P(A|C) = P(A n C) / P(C) = 0.05 / P(C)

Since A and C are independent events, we know that P(A|C) = P(A), so we can write:

0.05 / P(C) = 0.24

Solving for P(C) we get P(C) = 0.05/0.24 = 0.208

Alternatively, we can use the formula for the probability of the union of events:

P(A u B u C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C)

We know that P(A u B u C) = 1 - P((A u B u C)^/) = 1 - 0.33 = 0.67

and we know the values of P(A), P(B), P(A n B), P(A n C), P(B n C), P(A n B n C)

We can substitute these values into the above equation to find P(C)

P(C) = 0.67 - 0.24 - 0.26 + 0.05 + 0.05 + 0.05 - 0.02 = 0.208

So P(C) = 0.208

A. On the sixth day, the plant grows to 64 times its original height.

B. On the nth day, the plant would  [tex]2^n[/tex] time its original height.

A. From the given condition we can that the growth of the plant shows a geometric progression with a first term of 2 and a common ratio of 2.

On the first day, the plant grows to [tex]2^1[/tex] = 2 times its original height.

On the second day, the plant grows to [tex]2^2[/tex] = 4 times its original height.

Similarly, on the sixth day, the plant grows to [tex]2^6[/tex] = 64 times its original height.

B. The nth term of the progression can be calculated by multiplying the first term by the common ratio raised to the power of n-1.

In this case, the first term is 2 and the common ratio is 2. So the nth term is [tex]2 * 2^{n-1} = 2^n[/tex]

Hence, on the nth day, the plant grows to [tex]2^n[/tex] times its original height.

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The largest exterior angle of hexagone is 108°.

Given that exterior angle of a hexagon are x, 3x, 4x, 5x, 8x and 9x.

Exterior angles are those that run parallel to a polygon’s inner angles but are located outside of polygon.

We know that sum of exterior angle of any polygon is 360°.

So, sum of exterior angle of hexagon will be 360°.

x + 3x + 4x + 5x + 8x + 9x = 360°

30x = 360°

x = 360° / 30

x = 12°

Now the largest angle = 9 * 12 = 108°

Therefore, the largest angle of hexagon is 108°.

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The series converges to 16 * 3 = 48

A number series is a continues chain of number identical of non-identical depending on the logic behind the series. It can contain letters, number, variable, fraction, and numbers with power or exponents.

The series converges.

This series is in the form of 16 * (1 + 1/3 + 1/9 + 1/27 + ...)

The series 1 + 1/3 + 1/9 + 1/27 + ... is a geometric series with a common ratio of 1/3.

A geometric series converges if |r| < 1, where r is the common ratio. In this case, |1/3| < 1, so the series converges to lim (1/(1-1/3)) = 3.

So the series converges to 16 * 3 = 48

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The inverse of the function will be x=(4y-2)/(y+2) where x is the inverse of the function given in i.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x.

Now,

As given

f(x)=2(x+1)/4-x

from here x will be inverse of the function

Therefore

y(4-x)=2x+2

4y-yx=2x+2

4y-2=x(y+2)

x=(4y-2)/(y+2)

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The unit cost of an apple and a pear are $1.27 and $1. 98 respectively.

Algebraic expressions are defined as expressions that comprises of variables, factors, constants, terms and coefficients.

They are also made up of arithmetic operations like;

From the information given, we have that;

Let the apples be x

Let the pears by y

2x + 3y = 2.40

5x - 3y = 6.5

Let's solve the simultaneous equation

-1(2x + 3y = 2.40)

-2x - 3y = -2. 40

5x - 3y = 6.5

-2x - 5x = -2. 40 - 6.5

-7x = -8.9

x = $1.27

substitute the value for y

-2y -5(1.27) = -2.40

y = $1. 98

Hence, the values are $1.27 and $1. 98

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Answer:

C

Step-by-step explanation:

The shortest route from Ellport to Union Falls using road is 18 miles

An equation is an expression that shows the relationship between numbers and variables.

Pythagoras theorem is used to determine the measure of the sides of a right angled triangle. It is given by:

(hypotenuse side)² = (adjacent side)² + (opposite side)²

The distance from Larksville to Smithfield = 9 + 9 + 6 = 24 miles

The distance from Larksville to Union Falls = 19.5 + 6.5 = 26 miles

Let x represent the distance from Smithfield to Union falls, using Pythaoras:

26² = 24² + x²

x² = 100

x =  10 miles

the distance from Smithfield to Union falls is 10 miles.

Let y be the shortest route from Ellport to Union Falls, using Pythagoras:

y² = 10² + (9 + 6)²

y² = 10² + 15²

y² = 325

y = 18 miles

The distance from Ellport to Union Falls is 18 miles

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The number of terms in the algebraic expressions are:

From the question, we have the following parameters that can be used in our computation:

6y + 14 and 3x³ + 7x² + x - 5

Consider an expression given as

ax + b

The number of terms in the expression is 2 and the terms are ax and b

Using the above as a guide, we have the following:

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Complete question

Identify the number of terms and then the resend themselves for each algebraic expression

6y + 14 and 3x³ + 7x² + x - 5

Answer:

No

Step-by-step explanation:

It could only represent large colleges, not all colleges.  Sampling requires similar characteristics to represent the entire population of testing.

The measure of each angle are

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

<4 = 134

So, <4 = <2 = 134 (Vertical opposite angle)

<4= <8= 134 (Corresponding Angle)

<1 + <4 = 180 (Linear Pair)

<1 = 180-134

<1 = 46

<1 = <3= 46 (Vertical opposite angle)

<2= <6= 164 (Corresponding Angle)

<3= <7 (Corresponding Angle)

<1= <5 (Corresponding Angle)

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Answer:

b

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Because we are dealing with different units here, we first would need to know how many inches are in one foot.

1 foot = 12 inches

Now that we know how many inches are in a foot, we can convert the length and width of the room from feet to inches.

6 feet = 72 inches

10 feet = 120 inches

Taking these numbers, we now need to figure out the area of the floor.

72 × 120 = 8640

Now, find the area of each tile.

6 × 8 = 48

Taking 8640, we can now divide that by 48 to get the number of tiles needed.

8640 ÷ 48 = 180

Therefore, 180 tiles are needed to cover the floor.

Answer:

Slope is 3.5

There is a proportional relationship between the variables x and y

The other statements are false.

The slope is 3.5, not 7

A linear relationship is the same a proportional relationship so statement 4 is always false

The graph does pass through (0, 0)

Step-by-step explanation:

Consider the first 2 pairs of coordinates, (2, 7) and (6, 21);

The increase in x is from 2 to 6, i.e. an addition of 4, the increase in y is from 7 to 21, i.e. an addition of 14;

Now consider the the 2nd and 3rd pairs of coordinates, (6, 21) and (8, 28);

The increase in x is from 6 to 8, i.e. an addition of 2, the increase in y is from 21 to 28, i.e. an addition of 7;

So, with the first 2 pairs of coordinates, an increase of 4 in x resulted in an increase of 14 in y and with the second 2 pairs of coordinates, an increase of 2 in x resulted in an increase of 7 in y, i.e. (+4, +14) and (+2, + 7);

2 × (+2, +7) = (+4, 14)

Or:

(+4, +14) ÷ 2 = (+2, +7)

This means a line from the 1st point to the 2nd point and a line from the 2nd point to the 3rd point will have the same gradient:

To find the slope simple, find the increase in y resulting from an increase of 1 in x, so:

(+2, +7) ÷ 2 = (+1, +3.5)

The gradient (or slope) is 3.5;

If there is a line with a fixed gradient that passes through all the points, then the relationship is proportional, also linear;

This is the case for this question;

If we follow the pattern backwards as well, so the point:

(2, 7) - (+2, +7) = (0,0)

This means (0,0) lies on the line.

(0,0), (2, 7), (4, 14), (6, 21), (8, 28), (10, 35), (12, 42), (14, 49), etc.

All these points would lie on the line, just add 2 to x, add 7 to y;

You would find the same points plus others by the rule, add 1 to x, add 3.5 to y.

A function that gives the total cost, C in dollars, to be a member of the gym given the number of months, m is C = 7.99m + 30

The table that shows the total cost to be a member of the gym for different numbers of months is:

Number of Months     Total Cost

           3                        $53. 97

          6                         $77. 94

          12                        $125. 88

The rate of change of total cost per month would be,

m = [tex]\frac{77. 94-53. 97}{6-3}\\\\[/tex]

m = 7.99

so, the function for the total cost would be,

C = 7.99m + d          .......(1)

where d is the fixed cost of the gym

For m = 3, C = 53.97

53. 97 = 7.99m + d

53. 97 = 7.99(3) + d

d = 30

So, function (1) would be,

C = 7.99m + 30

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The slope is 2, which equals the distance travelled each hour. The total distance hiked at the start of the second day is represented by the y-intercept, which is 4, which is also the y-value. intercept's

We locate the rise/run before calculating the slope. Since the line increases by 2 between each point, the rise is 2. It travels over 1 between the points, hence the run is 1. The slope is now 2/1, or 2.

Given that it is rise/run, this gives us miles/hours, which indicates the number of miles she treks per hour.

The line's crossing of the y-axis is known as the y-intercept. At four, this is.

The fact that the y-value at this time is 4 and the x-value at this point is 0 tells us that she has trekked 4 miles in the 0 hours since the start of the second day, which is the distance she has covered so far.

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The surface area of the triangular prism is 120[tex]cm^2[/tex]

Now, According to the question:

A triangular prism is a polyhedron with a triangle for a base, thus it is a three-sided prism. Given that the triangle has three sides and a height of h, the surface area would be A = Ph + ab where P is the perimeter of the triangle.

We have :

A right triangular prism has a triangular base with legs of 5 centimeters and 12 centimeters and a hypotenuse of 13 centimeters.

Now,

Hypotenuse  = 13

a = 5 cm

b = 12 cm

h = 2 cm

The perimeter of the triangle is the sum of all the sides or:

P = 13 + 5 + 12

P = 30 cm

To get the surface area, substitute the values in the formula below:

A = Ph + ab

A = (30)(2) + (5)(12)

A = 60 + 60

A = 120

Hence, The surface area of the triangular prism is 120[tex]cm^2[/tex]

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The procedure that cannot be used are:

A. Knowing that 3² + 4² = 5², draw any two sides with a right angle between them. The third side will fit to form a right triangle.

B.

Knowing that 3 + 4 > 5, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

C.

Knowing that 3 + 5 > 6, draw the 3 cm side and the 5 cm side with a right angle between them. The 6 cm side will fit to form a right triangle.

The Pythagorean theorem states that the result obtained by squaring the value of the hypotenuse of a right angled triangle is equal to the sum of the squares of the values other two sides of the triangle.

The hypotenuse of a a given triangle is usually longer that the other two sides.

Therefore, the correct procedure when lengths such as 3 cm, 4 cm, 5 cm, and 6 cm should be knowing that 3² + 4² = 5², draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

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The solution of the given equation is 1.6. It has been represented and solved as a real-world problem below.

The given equation is = - 20 + 2x5 = 4

We can rewrite this equation as = - 4 + 2x5 = 20

Let us suppose that person A has x number of bananas that they have taken out from a stock full of bananas. They continue taking x number of bananas two more times. They then stop and see that person B has already taken 4 bananas from the stock. We can write this equation as -

= 4 + 2x

Person A saw knew that there were 20 bananas in total. So, we can write it as -

= 4 + 2x = 20

Person A then resumed and took x number of bananas again 5 more times. We can rewrite this as -

= 4 + 2x5 = 20

Solving this equation, we get -

= 4 + 10x = 20

= 10x = 20-4 = 16

= x = 16/10

= x = 1.6

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